Basic question that I can't find the answer to: Is there a way I can see a log/history of all the actions taken by KM in recent history?
Umm.. Keyboard Maestro Help Menu -> Open Logs Folder. Select Engine.log and it will open the Console.
Thanks! Do you know of a way where that Log could be automatically published/pushed to a site so I could check-in on what's happening with KM from my phone?
None that I know of, and I'm not sure you really want it.
Have you examined the KM Engine Log?
I find it very verbose containing a lot of entries that are, for the most part, inconsequential.
When you as for a log of "all KM actions", do you mean macros that have been executed? If so, that is available. There is no log of each Action within a Macro.
What is your purpose in viewing the log from an external device?
You could set up a remote trigger which copies the log file to Dropbox
This macro will show either the last Macro error, or, if no errors, the last 5 Macros that successfully executed. You could use it to build your own Macro to either save, or send, this log data somewhere that is accessible by your iPhone. For example, you could email a report, or save to a Cloud storage.
You could ran a Macro with a Periodic trigger as often as you think you need it.